Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Hughes B.D. — Random walks and random enviroments (Vol. 1. Random walks)
Hughes B.D. — Random walks and random enviroments (Vol. 1. Random walks)

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Random walks and random enviroments (Vol. 1. Random walks)

Автор: Hughes B.D.

Аннотация:

Volume 1 can be read without reference to Volume 2. In Volume 1, I expect of the reader only a modest facility in classical analysis, including the theory of functions of a complex variable up to contour integration. Those elements of probability theory which are needed are introduced in Chapter 1 of Volume 1, so that although an acquaintance with elementary
probability theory is helpful, it is not essential. Appendices to Volume 1 supply useful results involving special functions and some mathematical techniques which are useful in the study of random walks. Drawing only on Volume 1, a short course on the classical theory of random walks and their applications may be based on the core material of Chapter 1, §2.1- §2.2 of Chapter 2, and Chapters 3, 4, and 6, with a more substantial course drawing on some of Chapter 5, and additional material from Chapter 2. Chapters 1 and 7 are the basis of a course on the self-avoiding walk.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 631

Добавлена в каталог: 13.10.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
'Good' solvent      416
Abel's means, summation by      216
Absolutely continuous function      34
Absorbing boundary, continuum diffusion      228
Absorbing boundary, one-dimensional random walk      113
Alexander — Orbach scaling law      317 336
Allowed step      139
Amplitude function, self-avoiding walks and polygons      485
Amplitude function, structure function of Weierstrass random walk      214
Analytic continuation of spin dimension in n-vector model      535
Analytic continuation, familiarity assumed      569
Analytic continuation, precluded      218
Analytical chaos      5
Appell's function of fourth kind      583
Appell's Theorem      582
Asymptotic expansion      589
Attractive fixed point      518
Autocorrelation time in Monte Carlo simulation of self-avoiding walk walk      465
Average value      36
Bachelier's chain equation      207
Bachelier's equation      209
Backbone of a self-avoiding walk      431
Backward equations      251 280
Bailey's theorem      583
Bernoulli numbers      573
Bernoulli's theorem      54
Berretti — Sokal algorithm      466
Bessel function of imaginary argument      579
Bessel Function, First Kind      577—578
Bessel function, integrals involving      580—581
Bessel function, modified      579
beta function      572
Bethe lattice, correlated walk on      179
Bethe lattice, effectively infinite-dimensional      23
Bethe lattice, introduced      22
Bethe lattice, Polya walk on      113
Bipartite lattice, random walk on      336
Body-centred cubic lattice, Green function evaluated      605
Body-centred cubic lattice, return probability      153
Body-centred cubic lattice, structure function for      140
Boltzmann distribution      229 390
Boltzmann's constant      390
Bond Green function      303
Bond of a lattice      19
Bond percolation threshold      307
Bond-to-site transformation      496
Box dimension      15
Bravais lattice, defined      22
Bravais lattice, random walk on      136
bridges      429 436 445
Brillouin zone, first      137
Brownian motion      1 8 14 48 189
Brownian motion, generating self-affine set      17
Bubble diagram      446
Cacti, defined      25
Cacti, random walk on      179
Cantor (ternary) set      7
Cardinality of random walk      see "Number of distinct sites visited"
Catalan's constant      508
Cauchy density in winding angle problem      79
Cauchy density, defined      37
Cauchy density, example of stable density      198
Cauchy density, Fourier transform of      42
Cayley tree      see "Bethe lattice"
Cellular automata      5
Central Limit Theorem, analogue for $S_{n}$      359
Central Limit Theorem, Bernoulli's precursor of      54
Central Limit Theorem, Gram — Charlier refinements of      65 71
Central Limit Theorem, illustrated for one-dimensional Polya walk      64
Central Limit Theorem, introduced and stated      42—43
Central Limit Theorem, produces Gaussian density      189
Central Limit Theorem, sharp versions      197
Central Limit Theorem, three-dimensional version      91
Central Limit Theorem, two-dimensional version      70
Centre of mass of random walk      96
Chain equation      209
Chapman — Kolmogorov equation      207 209
Characteristic function      40
Chebyshev's inequality, stated and proved      44
Chebyshev's inequality, used      343
Clausen's Theorem, proved      582
Clausen's Theorem, stated      581
Clausen's Theorem, used      606
Coherent potential approximation      300
Collapse transition      515
Compact exploration      390
Compass dimension      15
Complementary events      31
Complete elliptic integral, an integral leading to      575
Complete elliptic integral, defined      575
Complete elliptic integral, evaluated via gamma functions      576—577
Complete elliptic integral, notational dangers      575
Complete elliptic integral, series expansion via Mellin transforms      592—593
Complete elliptic integral, series for      576
Complete elliptic integral, transformation of      576
Complete self-avoiding walks      507
Conditional mean first-passage time      126
Conditional probability      31
Conformal invariance      545
Connective constant for self-avoiding polygon      440
Connective constant for self-avoiding trail      495
Connective constant for self-avoiding walk      423
Connective constant, 'exact' for honeycomb lattice      426 428 436 481 544
Connective constant, estimates for dimension $\geq$ 4      490
Connective constant, estimates for three dimensions      483
Connective constant, estimates for two dimensions      482
Connective constant, inequalities for      426—436
Continuous-time random walk, analogue of Polya's Theorem      253
Continuous-time random walk, analysed by renormalization in one dimension      311
Continuous-time random walk, analysed by renormalization on Sierpinski lattice      314
Continuous-time random walk, analysed by renormalization on square lattice      313
Continuous-time random walk, diffusive      268
Continuous-time random walk, Montroll — Weiss model      243
Continuous-time random walk, Scher — Lax model      244 278—283
Continuous-time random walk, separable      244
Continuous-time random walk, subdiffusive      268
Continuous-time random walk, superdiffusive      268
Continuum double diffusion      225
Continuum resistance dimension      234
Convective diffusion equation      229
Convergence in probability      45
Convex function      45
Convex polygons (self-avoiding)      510
Convolution theorem for Fourier transform      40
Convolution theorem for Laplace transform      44
Convolution theorem for Mellin transform      591
Coordination number      20
Correction-to-scaling exponent      470
Correlated random walk      179
Correlation length for n-vector model, defined      528
Correlation length for n-vector model, exponents for      529
Countable      9
Covering lattice in Kasteleyn's walk problem      507
Covering lattice, defined      496
Covering lattice, significance in trail problem      496
Creeper, asymptotic behaviour      288
Creeper, defined      287
Creeper, model for turbulent dispersion      289
Critical amplitudes for self-avoiding walk      486
Critical exponent, n-vector model      525 527 529
Critical exponent, number of self-avoiding polygons      444
Critical exponent, number of self-avoiding trails      496
Critical exponent, number of self-avoiding walks      426
Critical exponent, structure function of Weierstrass random walk      213
Critical exponent, superdiffusive motion      199
Critical point in magnetic model      221
Critical point in method of steepest descent      100
Critical temperature in mean field treatment of magnetic model      533
Critical temperature in n-vector model      524
Cumulant generating function      374
Cumulants      373
Cumulative distribution function      33
Darboux's Theorem, stated      118
Darboux's Theorem, used      337 339 341 475
Debye's method      98
Decimated lattice      309
Decimated site      309
Decimation in renormalization analysis of random walk      309
Defective site in random walk      165
Delta function, Dirac's $\delta(x)$      9 28 33
Delta function, one-sided $\delta_{+}(x)$      33
Density of states, integrated      28 422
Density of states, vibrational      422
Denumerable      9
Detailed balance condition, generalized master equation      292
Detailed balance condition, master equation      290
Detailed balance condition, self-avoiding walk simulation      467
Deterministic chaos      5
Deterministic fractal      14
Devil's staircase      34
Dhar's formula      335
Diagmma function      572
Diamond lattice, Green function for      609
Diamond lattice, return probability      153
Dielectric constant, frequency-dependent complex      259
Dielectric constant, static      259
Diffusion constant for one-dimensional continuous-time random walk      268
Diffusion constant in diffusion equation      191
Diffusion equation with constant drift      191
Diffusion equation, derived in Fourier transform space      194—196
Diffusion equation, derived in real space      190—191
Diffusion equation, first-passage times      193
Diffusion equation, solved by Fourier transforms      191—193
Diffusion resistance      233
Diffusion-limited aggregation      398
Diffusive behaviour, loosely defined      284
Diffusive random walk      268
Dimension of a lattice      20
Dimension, based on resistance      233
Dimension, box      15
Dimension, compass      15
Dimension, continuum harmonic      234
Dimension, continuum resistance      234
Dimension, divider      15
Dimension, effective for random walk      157
Dimension, first-passage time      231 319
Dimension, fractal      13 210 336
Dimension, fractal, of a lattice      27
Dimension, fractal, of a self-avoiding walk      420—421
Dimension, fracton      30 317 336
Dimension, gap      17
Dimension, harmonic      29 30 335
Dimension, Hausdorff — Besicovitch      8 210 421
Dimension, intuitive      6
Dimension, local fractal      421
Dimension, mass      15 421
Dimension, reservations about terminology      9
Dimension, scaling      10
Dimension, scaling of a lattice      27
Dimension, spectral      30 336
Dimension, topological      7
Dimension, upper critical      422 534 541
Dimensional multiplicity      16
Dimensionally discordant set      13
Dimer problem      507
Dirac delta function      9 28 33
Directed lattices      20
Directed self-avoiding walks      491
Discrete Fourier Transform      40
Discrete Tauberian Theorem, analogue for Fourier series      160
Discrete Tauberian Theorem, misleading idea of accuracy      338
Discrete Tauberian Theorem, stated      118
Discrete Tauberian Theorem, used      128 130 141 334—336 338 340 355 362 368 474 490 539 601 603
Dispersion, relation      28
Dispersion, relative      271
Distribution function      33
Divider dimension      15
Domb — Joyce model      395
Double diffusion      225
Drag coefficient      229
Drunkard      1
Duplication formula      570
Dvoretzky — Erdos Lemma      332
Dyadic      see "Tensor"
Dyadic, use of boldface symbol      117
Effective dimension of a random walk      157
Effective medium approximation, basic formalism      300—304
Effective medium approximation, history      300
Effective medium approximation, single bond      304—308
Eigenfunction in lattice vibrations      134
Eigenfunction of operator $-\nabla^{2}$      230 386
Eigenvalue in renormalization      221
Eigenvalue of operator $-\nabla^{2}$      231
Eigenvalue of tensor A      143 355
Einstein — Smoluchowski relation for continuum diffusion      230
Enumeration techniques for self-avoiding walk      see "Series expansions"
Equilibrium configurations      391
Ergodicity of Monte Carlo algorithms      465
Euclidean space      6
Euler transformation      476
Euler walks      507
Euler's constant      570 573
Events, complementary      31
Events, independent      31
Events, introduced      30
Events, mutually exclusive      31
Excluded volume problem, defect of random flight model      98
Excluded volume problem, self-avoiding walk model      414
Expectation      36
Expected value      36
Face-centred cubic lattice, Green function evaluated      607
Face-centred cubic lattice, return probability      153
Face-centred cubic lattice, structure function for      140
Fick's law      228
Finitely ramified      514
First Brillouin zone      28 137
First-passage time density for continuous-time random walk      252
First-passage time density for diffusion equation      193
First-passage time dimension for continuum diffusion      231
First-passage time for diffusion equation      193
First-passage time for lattice walk      120
Fisher — Flory formula      451
Fisher's Lemma      455
Fixed point of an iterated mapping      518
Flory, P.J.      415
Fluctuation-dissipation theorem, 'proved'      528
Fluctuation-dissipation theorem, used      530
Forbidden site      168
Forward equations      251 280
Fourier sine transform      87 93
Fourier transform and moments      41
Fourier transform, defined      39
Fourier transform, discrete      40
Fourier — Bessel series, applied to Pearson's walk      72
Fourier — Bessel series, properties      578
Fractal dimension      336
Fractal dimension of Brownian motion trail      48 210
Fractal dimension of random walk trail      210
Fractal dimension of Weierstrass random walk trail      212
Fractal dimension, synonymous with Hausdorff — Besicovitch or scaling      13
Fractal lattice      25
Fractal sets      13
Fractal time      246—247
Fractals      13
Fracton dimension      30 317 336
Free energy of n-vector model      523
Free group      23
Gamma density, infinitely divisible but not stable      209
Gamma density, sum of random variables with exponential density      246
Gamma function, defined      569
1 2 3 4
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте